KIND OF!!!
In order to make this work, you should make sure the website is loaded on your computer before you get to your competition location (IE do this at home or using a hotspot). IF the site is blocked at the competition locations WIFI, you should be able to keep the site loaded up for use. But this only works if its already loaded up.
DON'T HIT REFRESH!! When the browser tries to reload the debatevibe app it will run into the WIFI blocking it and will prevent it from working!
The best bet is to ask the tournament host to ensure that the debatevibe app url is unblocked by the WIFI.
You could..... I'm not sure file production would be super convinent for people as it would be a lot of downloading and importing of files to create savepoints of work done within DebateVibe. I would suggest, at this time, to utilize the system discussed on the Without Verbatim Page